Why Rounding Is Sometimes Wrong: Significant Figures and Error Accumulation
Round at every step and the final result drifts. Understanding error accumulation and banker's rounding makes your calculations trustworthy. Read the full guide with step-by-step examples and practical tips.
Rounding is the first rule taught in school, yet in chained calculations or large datasets, mechanical rounding introduces systematic bias and accumulated error.
Problem one: don't round intermediate steps
Compute 1.4 × 2.6 × 3.8, rounding to one decimal each step: 1.4 × 2.6 = 3.64 → 3.6, then 3.6 × 3.8 = 13.68 → 13.7. Computed directly, 1.4 × 2.6 × 3.8 = 13.832 → 13.8. Rounding mid-way shifted the result by 0.1.
Problem two: rounding has systematic bias
Digits 1–4 round down and 6–9 round up, which looks fair, but the treatment of 5 gives one extra case to rounding up. Across large datasets that makes results systematically too high.
Statistics more often uses “round half to even” (banker's rounding): below 5 rounds down, above 5 rounds up, and exactly 5 goes to the nearest even number. Over many values, positive and negative biases cancel out.
- 2.5 → 2 (toward the even number)
- 3.5 → 4 (toward the even number)
- 1.24 → 1.2
- 1.26 → 1.3
What significant figures are
Significant figures are the digits counted from the first non-zero digit, and they express the precision of a measurement or calculation. 0.0052 has two significant figures; 5.20 has three. A trailing zero isn't decorative — it says that zero was actually measured.
Rules of thumb: for addition and subtraction, match the fewest decimal places; for multiplication and division, match the fewest significant figures.
Using it day to day
The Rounding Calculator handles a variety of rounding needs. Be especially careful with financial data: currency calculations typically specify two decimals, and you should round the final result rather than every intermediate amount.